Problem: Simplify the following expression: $\sqrt{32}+\sqrt{18}+\sqrt{50}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{32}+\sqrt{18}+\sqrt{50}$ $= \sqrt{16 \cdot 2}+\sqrt{9 \cdot 2}+\sqrt{25 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{2}+\sqrt{9} \cdot \sqrt{2}+\sqrt{25} \cdot \sqrt{2}$ $= 4\sqrt{2}+3\sqrt{2}+5\sqrt{2}$ Finally, simplify by combining the terms. $= ( 4 + 3 + 5 )\sqrt{2} = 12\sqrt{2}$